1. Field of the Invention
The present invention relates, in general, to an apparatus and method for deforming a curved surface using a three-dimensional target curve and, more particularly, to an apparatus and method for deforming the curved surface of a non-uniform rational B-spline model on the basis of a three-dimensional target curve input by a user.
2. Description of the Related Art
Three-dimensional graphics have been widely applied in various fields, such as the production of movies, as well as the implementation of games, Computer Aided Design (CAD), animation, and virtual reality. A representative method of implementing three-dimensional graphics is polygon modeling. Such polygon modeling is based on solid modeling and denotes a scheme of implementing a desired shape by dividing or combining respective closed solids, all surfaces of which are closed. However, in order to represent a slightly curved surface, a great number of polygons is required depending on the extent of variation in the curvature of a curved surface, or the level of detail of an operation, so that there is a problem in that the final amount of data is excessively increased.
Due to such a problem, concern about Non-Uniform Rational B-Spline (NURBS) modeling has recently been highlighted. NURBS is an improved method of mathematically representing a three-dimensional curve, and is a modeling method capable of precisely defining, in particular, a non-uniform curve or surface.
In NURBS modeling, an object is not represented through sampling, but is represented by numerical formulas using control points and knot vectors. The control points are points used to represent the shape of a curved surface in a manner similar to that of a Bezier curve, which is used to represent computer fonts, etc. Knot vectors are required to prevent a problem in which the overall shape of a curved surface is changed due to the movement of a single point at the time of adjusting the shape of a curved surface, that is, a shape in which local adjustment is impossible, and are used to adjust only a portion of the curved surface, influenced by the knot vectors, among the entire curved surface, even if control points are changed. The use of such NURBS modeling confers many advantages in that more precise representation is possible depending on the hardware that is used, and gentle and smooth motion can be represented through the adjustment of parameters.
A principal operation in three-dimensional modeling can be referred to as an operation of deforming a curved surface. Methods of deforming a model can be broadly classified into an indirect deformation method (1) of deforming a model, as in the case of free-form deformation of a solid model by Seberberg & Parry, and a direct deformation method (2) of directly deforming a model, as in the case of direct manipulation in free-form deformation by Hsu, Hughes & Kaufman [(1) Free-Form Deformation of Solid Geometric Models, Proceedings of SIGGRAPH'86, Computer Graphics, p 151-p 160, 1986]/[(2) Direct Manipulation of Free-Form Deformations, Proceedings of SIGGRAPH'92, Computer Graphics, p 177-p 184, 1992].
The indirect deformation method, which deforms a model according to the deformation of a grating, is disadvantageous in that it is difficult to use to implement precise deformation, and it is not intuitively grasped by a user. In contrast, the direct deformation method is advantageous in that it allows a user to intuitively deform a model, but is disadvantageous in that, in order to deform a model into a desired form, a lot of time and expense are required to learn the usage method thereof, and the user must undergo a lot of trial and error.
Meanwhile, a method of a designer (or a user) expressing his or her thinking in a planar sketch is implemented by basically representing the contour, texture or feature of an object using curves. From the standpoint of a designer, such an operation method is implemented as drawing habits through use and education over a long period of time.
However, the plurality of graphic tools employing NURBS modeling does not sufficiently consider the drawing habits of a designer. Therefore, the operation of deforming a model is problematic in that it is not intuitively used by a designer and, moreover, a series of deformation methods defined by graphic tools must be learned for a long period of time.